Double wing vortex flowmeter with strouhal number corrector

ABSTRACT

A vortex flowmeter includes a body having a flow passage, a vortex generator that generates a standing transverse wave in the flow passage, and first wing and second wings in the passage downstream of the generator. A circuit that utilizes sensors in the two wings is provided for first determining an operational phase difference, Δφ m  between the signals representing movement of the first and second wings. A microprocessor then determines a corrected vortex frequency,  f  corr, in response to a ratio of a predetermined calibration phase difference Δφ c  to the measured phase difference Δφ m .

This application is a continuation-in-part of application Ser. No.08/046,047, filed Apr. 9, 1993, now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to a meter for measuring fluid flow by detectingKarman vortices, In particular, the invention is an improved vortexflowmeter that compensates for changes in the Strouhal Number,dimensional changes of a bluff body, or for measurement error associatedwith conditions in a pipe which distort the fluid velocity profile.

The accuracy of vortex flowmeters depends in part on using a propervalue for the Strouhal Number, N_(s). The Strouhal Number is anon-dimensional flow number that is related to the stability of fluidflow when an obstruction is placed in the flow. Once the Strouhal Numberis determined or calibrated for a particular vortex flow meter, ittypically remains constant when the meter operates. This means that theStrouhal Number can usually be pre-determined before installationwithout sacrificing flowmeter accuracy. However, the Strouhal Numberchanges substantially at very high (i.e. 2,000,000) or very low (i.e.20,000) Reynold's Number, R_(e). It also makes an apparent change whenpiping conditions are altered from ideal conditions, which isillustrated by small errors in measurement. In these circumstances, orany other circumstances where the Strouhal Number changes afterinstallation, a vortex flowmeter might not be accurate.

The accuracy of vortex flowmeters also depends in part on using theproper characteristic dimension for an obstruction (i.e., a bluff body)placed in the flow path. As vortex flowmeters operate over time, theseobstructions tend to erode and their characteristic dimension changes,In time, this causes vortex flowmeters to be inaccurate.

In addition, the accuracy of ordinary vortex flowmeters depends on thevelocity profile of the fluid as it approaches and impinges on the bluffbody. For vortex flowmeters to be accurate, it is usually required thatthe velocity profile be fully developed. Certain portions of piping suchas elbow or expanders distort a velocity profile. Therefore, an ordinaryvortex flowmeter should be installed only after many pipe diameters ofstraight pipe. This can be a burdensome requirement. Especially sincevelocity profiles can be distorted not only after pipe bends, but alsowhen internal pipe diameters are mismatched at pipe joints, or even whenthe friction factor of pipe walls changes.

In general, the operation of vortex flowmeters is well known. Anelongated obstruction, called a bluff body, is placed transverse to thedirection of fluid flow within a conduit and generates vortices in itswake. The vortices are induced by and shed alternately from oppositesides of the bluff body. This is the Karman effect. The frequency ofvortex shedding is inversely proportional to the width of the bluff bodyand directly proportional to the velocity of the flow, so that detectingthe frequency generates signals indicative of fluid flow velocity. Themeasured fluid flow velocity past the bluff body, V_(m), is described bythe equation: ##EQU1## where N_(s) is the Strouhal Number, f_(m) is themeasured shedding frequency, and D is the diameter or width of the bluffbody.

Vortices are generated in pairs, often referred to as two rows, and aredisposed on either side of the longitudinal axis of the bluff body. Therotational direction of the individual vortices is such that eachreinforces the other and combines with the other. As the vorticesproceed away from the bluff body, the result is loss of individualcharacter for each vortex and the creation of sinusoidal-like fluidmotion transverse to the direction of the velocity of the fluid. Ineffect, the vortices form a standing transverse wave beyond the bluffbody with the wavelength given by: ##EQU2## where V is the actual fluidflow velocity past the bluff body, and f_(vor) is the actual sheddingfrequency.

The sinusoidal-like wave is persistent, with normally expecteddissipation, unless disrupted by some mechanical means. In general, thestrength of the vortices increases with increased velocity and withincreased fluid density in the relationship of ρV².

A variety of means for detecting vortices have been proposed, includingthe use of acoustic detection (U.S. Pat. No. 3,886,794 issued Jun. 3,1975 to McShane), hot wires (U.S. Pat. No. 4,275,602 issued Jun. 30,1981 to Fujishiro, et al), and a physical member located downstream ofthe obstruction and subject to deflection as alternating vortices passby. In this latter approach, the physical member often takes the form ofa wing and the wing may either be pivotably mounted in the conduit (U.S.Pat. No. 3,116,629 issued Jan. 7, 1964 to Bird and U.S. Pat. No.4,181,020 issued Jan. 1, 1980 to Herzl) or be fixed to the conduit (U.S.Pat. No. 4,699,012 issued Oct. 13, 1987 to Lew, et al). In co-pendingU.S. patent application Ser. No. 07/813,875, filed on Dec. 19, 1991,Vander Heyden, et al. disclose a double wing vortex flowmeter that makesflow measurements which are substantially unaffected by externalvibrations.

A major shortcoming with present day vortex flowmeters is that they aresometimes inaccurate because the measured fluid flow velocity V_(m) asdetermined by the measured shedding frequency f_(m), depends on theStrouhal Number N_(s), the characteristic dimension of the bluff body D,and on the fluid velocity profile; and present day vortex flowmeters donot compensate for changes in these conditions which may occur afterinstallation. The present invention improves the accuracy of vortexflowmeters by compensating flow measurements for changes that may occurin these conditions after installation.

SUMMARY OF THE INVENTION

In accordance with the invention, a vortex flowmeter includes a bodyhaving a flow passage, an elongated vortex generator in the flow passagetransverse to the direction of flow through the passage, a first wing inthe passage downstream of the generator, and a second wing in thepassage downstream of the first wing. The vortex generator generates astanding transverse wave. A sensor is associated with each wing toprovide a signal in response to the movement of each wing. Means areprovided for determining a phase difference Δφ_(m) between the signalsrepresenting movement of the first and second wings.

It is preferred that the invention determine fluid velocity, V_(m), inaccordance with ##EQU3## where Δφ_(m) is a phase difference determinedduring flowmeter operation, Δφ_(c) is a calibrated phase differencedetermined before operating the flowmeter, f_(m) is a vortex sheddingfrequency, D is a characteristic dimension associated with the vortexgenerator as determined before operating the flowmeter and N_(si) is aninitial Strouhal Number as determined before operating the flowmeter. Ina preferred embodiment, the phase difference Δφ_(m) is determined usinga circuit or microprocessor.

In the above equation, the expression ##EQU4## can be replaced by asingle expression f_(corr), representing the corrected vortex frequency.

The sensors may take a variety of forms, including thermal, optical, andpressure sensitive sensors. Preferably, the sensors are piezoelectrictransducers which may be mounted within the wings.

The invention also resides in a method of measuring flow through a flowpassage which includes the steps of using a vortex generator with acharacteristic dimension D to generate rows of vortices in the flowpassage to form a standing transverse wave flow pattern beyond thevortex generator, detecting the vortices at one position in the flowpassage, detecting the vortices at a second position in one flow passagedownstream from the first position, generating a sisal at each detectionposition representative of the frequency of the vortices at thatposition, determining a phase difference Δφ_(m) between the first andsecond positions of the standing transverse wave from the generatedsignals, determining a vortex shedding frequency f_(m), and multiplyingthe vortex shedding frequency f_(m) by a predetermined constant(preferably ##EQU5## and by the phase difference Δφ_(m).

A principal object of the invention is to provide an extremely accuratevortex flowmeter.

Another object of the invention is to provide a vortex flowmeter thatsubstantially eliminates errors in measurement resulting from changes inthe Strouhal Number or erosion of the bluff body.

Yet another object of the invention is to provide a vortex flowmeterwith improved immunity from inaccuracies caused by non-uniform velocityprofile.

The foregoing and other objects and advantages .of the invention willappear in the following detailed description. In the description,reference is made to the accompanying drawings which illustratepreferred embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a longitudinal view in vertical section taken through aflowmeter in accordance with the present invention;

FIG. 2 is a view in vertical cross-section taken in the plane of theline 2--2 of FIG. 1;

FIG. 3 is a view in longitudinal section taken in the plane of the line3--3 of FIG. 1;

FIG. 4 is a schematic diagram showing a circuit that determines a phasedifference in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The vortex flowmeter includes a body 10 of relatively rigid constructionso that it will move as a unit when subjected to external forces such asvibrations. The flowmeter body 10 is adapted to be inserted in thepiping for the flow of fluid which is to be measured. The body 10defines a flow passage 11 of circular cross-section. An obstruction 12in the form of an elongated bluff body is disposed across the flowpassage 11 and along the longitudinal axis 13 of the flow passage. In aknown manner, the obstruction 12 will function as a vortex generatorproducing vortex rows on either side of the longitudinal axis.

Downstream of the vortex generator 12 within the flow passage 11 is afirst wing 15 that is rigidly attached at its top to the body 10.Alternatively, the wing 15 can be attached to the body 10 through a softflexible member. The first wing 15 extends downwardly transverse to thedirection of flow through the passage 11 and through the longitudinalaxis 13. The bottom end of the wing 15 is free of the body 10 so thatthe first wing 15 is cantilevered within the flow passage 11. A secondwing 16 identical in construction to the first wing 15 is disposeddownstream of the first wing 15.

Both of the wings 15 and 16 contain internally embedded sensors 18 and19, respectively. The sensors 18 and 19 are in the form of piezoelectrictransducers. The sensors 18 and 19 are of known construction and theycomprise a piezoelectric ceramic which, when subjected to strain, willproduce a voltage signal indicative of the strain. Useable ceramicswould be those made by Keramos, Inc. of Indianapolis, Ind. andidentified as Kezite K15 and K350 ceramics. When a wing 15 or 16 isdisplaced by vortex activity, the associated sensor 18 or 19 issubjected to strain and the sensor produces a signal related to thevortex activity. The signal from each sensor 18 and 19 is continuouslyrelayed to a microprocessor 22 where the vortex activity is analyzed.

Referring to FIG. 3, the vortices V shed from the vortex generator 12.The spacing between vortices depends on the characteristic dimension Dof the vortex generator 12 and the Strouhal Number N_(s) of the flow.Although the vortices are independently shed from either side of thevortex generator 12, Von Karman showed that stable shedding can existonly if the swirl of each vortex reinforces its opposite partner. It istherefore useful to consider that oppositely shed vortices form adynamic wave oscillating to and fro across the areas of the wings 15 and16. This is illustrated schematically in FIG. 3 by the wave 20. Althoughthe wave 20 in FIG. 3 is illustrated as being a regular sinusoidalcurve, in reality the wave would be very chaotic and somewhathyperbolic. The two wings 15 and 16 are preferably disposed within thepaths of the vortex street such that the wings will be subjected todeflections caused by the vortices that are 180 degrees out of phase.The reasons for this are explained in a co-pending patent applicationfiled by Vander Heyden, et al. on Dec. 19, 1991, Ser. No. 07/812,815. Inorder that the wings 15 and 16 be subjected to deflections caused byvortices 180 degrees out of phase with each other, the wings 15 and 16are spaced apart a distance W which should be a multiple of a half wavelength, i.e. n1/2λ of the vortex street generated by the vortexgenerator 12. Thus, while one wing is being deflected by the vortices inone direction the other wing will be deflected in the opposite directionrelative to the longitudinal axis 13.

Under ideal conditions, the fluid velocity V_(m) can be measured bymeasuring the shedding frequency f_(m) and using the following relation:##EQU6## where D is the characteristic diameter of the bluff body 12 andN_(si) is the Strouhal Number as determined under ideal conditions. Theshedding frequency f_(m) can be continuously determined in themicroprocessor 22 by analyzing a signal from either sensor 18 or 19 asis generally known in the art. Under ideal conditions, thecharacteristic diameter D of the bluff body, and the Strouhal NumberN_(si) are known and are constant. However, inaccuracies can ariseduring operation when either the characteristic diameter D erodes or theStrouhal Number N_(s) fluctuates or drifts. The present inventioncompensates for these inaccuracies by continuously monitoring signalsfrom sensors 18 and 19 to determine an actual phase difference Δφ_(m)between the signals, and uses this value to adjust Eq. (1).

The wavelength λ of the standing transverse wave that forms beyond thebluff body is given by: ##EQU7## The wavelength λ varies with changes inthe characteristic dimension of the bluff body and changes in theStrouhal Number N_(s) that may occur during operation of the flowmeter.Referring to FIG. 3, the second wing 16 is located a distance Wdownstream of the first wing 15. The phase difference Δφ of the vortexwave between the first wing 15 and the second wing 16 is represented by:##EQU8## where the phase difference Δφ is determined in radians. Theactual phase difference Δφ_(m) between the first and second wing can bedetermined in the microprocessor 22 by comparing the vortex activity ateach wing 15 and 16 using conventional techniques. FIG. 4 shows thelogic of a circuit 25 for determining the actual phase differenceΔφ_(m),

Referring to FIG. 4, signals S₁ and S₂ from sensors 18 and 19,respectively, are combined in the circuit 25 to determine the actualphase difference Δφ_(m). Signals S₁ and S₂ are generallysinusoidal-like, but S₂ is about 180 degree out of phase with S₁ becausesensor 19 is placed about one-half of wavelength downstream of sensor18. Charge amplifiers 23 and 24 may be necessary to amplify the signalsS₁ and S₂ from sensors 18 and 19 before the signals are analyzed in thecircuit 25. The amplified signal S₁ is converted into an inverted squarewave D₁ by an analog to digital inventor/convertor gate 26. The invertedsquare wave D₁ is a binary representation over time indicating when thesensor 18 is displaced from a neutral position. The amplified signal S₂is converted into a square wave D₂ by an analog to digital convertorgate 27, but the signal S₂ is not inverted. The square wave D₂ is abinary representation over time indicating when the sensor 19 isdisplaced from a neutral position.

The square waves D₁ and D₂ are compared in a logical "exclusive-or" gate28. The output from the "exclusive-or" gate 28 can be described as astep function having a low value when the signals D₁ and D₂ arecontemporaneously high, or contemporaneously low; and a high value whenD₁ and D₂ are out of phase. The output from the "exclusive-or" gate 28is then compared to the inverted square wave D₁ by a logical "and" gate29 to determine whether signal D₁ trails or precedes signal D₂. Theoutput from the "exclusive-or" gate 28 is also provided to a low passfilter 30 to determine the magnitude of the phase difference between D₁and D₂. A low pass filter 30 is sufficient for this purpose becausechanges in the measured phase difference Δφ_(m) are slow compared tovortex frequency. The value of Δφ_(m) can thus be determined in arelatively continuous manner by monitoring the output of the logical"and" gate 29 and the low pass filter 30.

It should be appreciated that there are other ways known in the art fordetermining a phase difference between two waves. Any of these methodsshould be sufficient for the present invention.

Under ideal conditions before the flowmeter is installed in the field,such as in a laboratory, the characteristic dimension D and the idealStrouhal Number N_(si) are known and the wavelength λ of the standingwave under ideal conditions can be measured using Eq. (2). The secondwing 16 is then placed at a distance equal to one halt λ downstream ofthe first wing 15. The meter can then be tested in the laboratory todetermine a calibrated phase difference Δφ_(c) between the first andsecond wings. The value for Δφ_(c) should be about 180° since the secondwing 16 is preferably placed about one half λ downstream of the firstwing 15.

After the flowmeter has been installed in the field for operation, theactual phase difference Δφ_(m) between the two wings 15 and 16 iscontinuously measured. The actual phase difference Δφ_(m) between thefirst 15 and second 16 wings can vary with changes in the characteristicdimension D of the bluff body, with changes in the Strouhal NumberN_(s), and with changes in the fluid velocity profile caused because ofinstallation conditions. In fact, referring to Eqs. (2) and (3), it canbe seen that variations in the phase difference Δφ_(m) are such that:##EQU9## where ##EQU10## is the ratio of the characteristic diameter ofthe bluff body to the Strouhal Number at the time Δφ_(m) is measuredduring operation, and ##EQU11## is the same ratio but determined bytesting and calibration before installation.

Equation (1) which is for ideal conditions can therefore be adjusted tocorrect for variations in the characteristic dimension D of the bluffbody, the Strouhal Number N_(s), or the velocity profile byincorporating the ratio ##EQU12##

In accordance with Equation (5), the vortex flowmeter measures the fluidvelocity V_(m) by continuously measuring both the vortex sheddingfrequency f_(m) and the phase difference Δφ_(m) of the standingtransverse wave between the two wings 15 and 16. The meter thusaccurately measles fluid velocity V_(m) by continuously compensating forvariation in the characteristic dimension of the bluff body, thevelocity profile, or the Strouhal Number N_(s).

When the actual phase difference Δφ_(m) becomes much different than π(i.e. 180°), the bluff body is ruined and should be replaced.

Although the invention is shown as incorporating piezoelectrictransducers as the sensors, other forms of sensors could be employed,including other forms of pressure sensors. For example, the movement ofthe wings could be detected optically or acoustically.

The term "wings" as used in this application is not meant in a limitingsense and is not meant to define a particular shape or structure.Instead, the term is used to refer to any physical element imposeddownstream of the vortex generator that will be subjected to deflectionby the vortex streets.

I claim:
 1. A vortex flowmeter comprising:a body having a passage for flow of a fluid therethrough in a longitudinal direction; a vortex generator positioned in the passage for transmitting vortices downstream; a first vortex sensor located at a first sensor position downstream of the vortex generator, the first vortex sensor producing a first signal of the vortex frequency, f_(m), in response to passage of vortices through the first sensor position; a second vortex sensor located at a second sensor position downstream of the vortex generator, the second vortex sensor producing a second signal of the vortex frequency, f_(m), in response to passage of vortices through the second sensor position, said second signal being phase delayed from said first signal; means for determining a measured phase difference Δφ_(m) between the first signal and the second signal; and means for comparing the measured phase difference Δφ_(m) to a calibration phase difference Δφ_(c) representing the phase difference between the first sensor position and the second sensor position wing under pre-operational, calibration conditions; means for determining a corrected vortex frequency, f_(corr), of said flow meter during operation in response to a ratio of the predetermined calibration phase difference Δφ_(c) to the measured phase difference Δφ_(m).
 2. The vortex flow meter of claim 1, whereinthe first vortex sensor is located in the passage in a first wing downstream of the vortex generator; and wherein the second vortex sensor is located in the passage in a second wing downstream of the vortex generator.
 3. The vortex flowmeter of claim 2, wherein the sensors are piezoelectric transducers.
 4. The vortex flowmeter of claim 2, wherein the means for determining the measured phase difference, Δφ_(m), comprises a circuit for comparing the signals from the first and second vortex sensors located in the first and second wings, respectively.
 5. The vortex flowmeter of claim 1, further comprising means for determining a fluid velocity V_(m) in accordance with the following relation: ##EQU13## where Δφ_(m) is the determined phase difference, Δφ_(c) is a calibrated phase difference between the first and second wings as determined before operating the flowmeter, f_(m) is the vortex frequency, D is a characteristic length associated with the vortex generator as determined before operating the flowmeter, and N_(si) is the initial Strouhal Number as determined before operating the flowmeter.
 6. The flowmeter of claim 1 wherein the calibration phase difference Δφ_(c) is predetermined to be 180°.
 7. A method of determining a fluid velocity V_(m) of fluid flowing through a flow passage comprising:using a vortex generator with a characteristic dimension D to generate rows of vortices in the flow passage to form a standing transverse wave flow pattern; detecting the vortices at one position in the flow passage; detecting the vortices at a second position in the flow passage located downstream from the first position; producing a first signal of a vortex frequency, f_(m), in response to detecting the vortices at the first detection position; producing a second signal of a vortex frequency, f_(m), in response to detecting the vortices at the second detection position; determining a phase difference Δφ_(m) between the first and second signals; determining measured fluid velocity V_(m) by obtaining a corrected vortex frequency, f_(corr), by multiplying the vortex frequency, f_(m), by the ratio of the predetermined calibration phase difference Δφ_(c) to the measured phase difference Δφ_(m).
 8. The method of claim 7, wherein the fluid velocity V_(m) is further obtained by multiplying the correction frequency, f_(corr), by the ratio of ##EQU14## where D is the characteristic diameter of the vortex generator as determined before operation, and N_(si) is the initial Strouhal Number as determined before operation.
 9. The method of claim 7, wherein the second position is located downstream from the first position a distance that is an odd multiple of half of a wavelength of the standing transverse wave.
 10. A method as recited in claim 7 wherein the phase difference Δφ_(m) is determined by:continuously transmitting the generated signals to a circuit; and analyzing the continuously transmitted signals in the circuit. 